- International Electronic Journal of Geometry
- Vol: 11 Issue: 2
- A Curvature Energy Problem on a Timelike Surface
A Curvature Energy Problem on a Timelike Surface
Authors : Gözde Özkan Tükel, Ahmet Yücesan
Pages : 120-125
Doi:10.36890/iejg.545141
View : 5 | Download : 3
Publication Date : 2018-11-30
Article Type : Research
Abstract :We present a variational study of finding null relaxed elastic lines which are extremals of a geometric energy functional, subject to suitable constraints and boundary conditions on a timelike surface in Minkowski 3-space. We derive an Euler-Lagrange equation for a null relaxed elastic line with regard to geodesic curvature, geodesic torsion and normal curvature of the curve on the timelike surface. Finally, we give some examples for null relaxed elastic lines on the pseudo-sphere and pseudo-cylinder.Keywords : Null relaxed elastic line, Euler-Lagrange equation, variational calculus